End Mill Having A Symmetric Index Angle Arrangement For Machining Titanium

ABSTRACT

An end mill for machining titanium includes a cutting portion having blunt cutting edges alternated with flutes. Each flute includes, in order from the cutting edge, a rake surface, a concavely shaped bending portion, a convexly shaped ejecting portion and a tooth relief edge. The convexly shaped ejecting portion has an ejection height E, which is measurable between an apex of the ejecting portion to an imaginary straight line extending from a nadir of the adjacent bending portion of the flute to the adjacent tooth relief edge. In a plane perpendicular to a rotation axis of the end mill, the ejection height E and a cutting portion diameter D E , fulfill the condition 0.010D E &lt;E&lt;0.031D E .

FIELD OF THE INVENTION

The subject matter of the present application relates to end millsconfigured for machining titanium.

BACKGROUND OF THE INVENTION

Titanium can be considered a relatively difficult material to mill asthe properties thereof can quickly degrade an end mill. Such degradationis believed, in theory, to be at least in part due to heat transfer of aworkpiece made of titanium to an end mill machining the workpiece.

Aside from heat transfer, another consideration when designing end millsis evacuation of chips. Flute shape is accordingly taken into accountduring end mill design. CN 20145538, CN 102303158 and CN 202199817disclose end mills having flutes shape in accordance with differentmathematical models.

Yet another consideration is reduction of end mill chatter. Reduction ofchatter can be achieved, in theory, by designing end mills withasymmetric features, for example, as disclosed in U.S. Pat. No.6,991,409, U.S. Pat. No. 7,306,408 and U.S. Pat. No. 8,007,209. FIG. 1of U.S. Pat. No. 8,007,209 also disclosing an end mill having serrations(FIG. 1, reference numeral 7).

While many end mills appear similar, upon close inspection there areoften many small but relevant differences, some differences beingcritical as to whether an end mill can achieve a desired machiningoperation of a particular type of material or under particular cuttingconditions.

Commonly, cutting edges are placed at different index angles withrespect to each other, helix, radial rake and axial rake angles may varyat different cutting edges and even may vary along a single cuttingedge. Orientation, position and size of each element in an end mill mayhave significant effect on the performance thereof.

In view of the extremely large number of variations of design possible,there is ongoing research to try and find more efficient end mills,especially for machining specific materials such as titanium.

SUMMARY OF THE INVENTION

It has been found that an end mill combining a particular tooth shapeand a particular flute shape can achieve surprising longevity whenmachining titanium under certain conditions.

More precisely, the tooth shape comprises a blunt cutting edge (thecutting edge being at an intersection of a rake cutting sub-surface anda relief surface) and a recessed rake sub-surface (hereinafter a “rakerecessed sub-surface”) extending from the rake cutting sub-surface.

While blunt cutting edges could be considered detrimental, due torelatively increased machining power requirements caused thereby,experimental results have shown otherwise.

More precisely, a blunt cutting edge is defined as having an actualinternal cutting angle formed at an intersection of a rake cuttingsub-surface and a relief surface, the actual internal cutting anglehaving a greater value than an imaginary internal cutting angle formedat an intersection of imaginary extension lines of the rake recessedsub-surface and the relief surface.

It will be understood that use of the term “blunt” when referring to acutting edge hereinafter is interchangeable with the definition above.

Provision of a rake recessed sub-surface adjacent a rake cuttingsub-surface (i.e. the rake recessed sub-surface adjacent being recessedfurther into a tooth than an adjacent rake cutting sub-surface relativeto an imaginary radial line passing through the cutting edge, or, stateddifferently, the rake cutting sub-surface being raised above the rakerecessed sub-surface relative to an imaginary radial line passingthrough the cutting edge), is believed, in theory, to reduce heattransfer to an end mill when machining titanium.

Similarly, minimizing the length of a rake cutting sub-surface is alsobelieved to reduce heat transfer by reducing contact of chips with anend mill rake surface.

Referring now to the above-mentioned flute shape, the flute comprises aconcavely shaped bending portion followed by a convexly shaped ejectingportion of a particular size.

The bending portion is configured for bending titanium chips during amilling operation. A flute comprising a bending portion is illustratedin FIG. 4 of CN 102303158.

Generally speaking, convexly shaped flute portions can providestructural strength to a tooth (i.e. allowing increased thicknessthereof) and increased moment of inertia. The presence of such convexportion, however, reduces a flute's cross-sectional shape which isbelieved to be detrimental to chip evacuation from the flute. A flutewithout such convex portion is illustrated in FIG. 3 of CN 102303158.

It has now been found that provision of a convex portion, albeit of aspecific size can provide an advantageous chip ejection effect duringmachining of a titanium workpiece (consequently, the convexly shapedportion of the subject matter of the present application is entitled an“ejecting portion”). More precisely, it has been found that suchejecting portions provide better machining performance during titaniumslotting operations which have limited space for chip evacuation, withparticularly good results shown at relatively high titanium machiningspeeds.

A further consideration when machining titanium is reduction of chatter,typically by asymmetric features of an end mill. Despite perceivedbenefits of asymmetry, an end mill having a symmetric index anglearrangement was found to have comparative longevity.

For the purposes of the specification and the claims, an end mill with asymmetric index angle arrangement is defined as one where, at a cuttingend face, every flute has an index angle value identical to an indexangle value of an opposing flute. Conversely, an end mill with anasymmetric index angle arrangement is one which does not fall withinthis definition.

In accordance with a first aspect of the subject matter of the presentapplication, there is provided an end mill for machining titanium, theend mill comprising a cutting portion having teeth alternated withhelically shaped flutes and a cutting portion diameter D_(E); each toothcomprising a blunt cutting edge formed at an intersection of a rakecutting sub-surface and a relief surface, and a rake recessedsub-surface recessed in the tooth more than the rake cuttingsub-surface; each flute comprising, in a plane perpendicular to arotation axis of the end mill, a concavely shaped bending portionconnected to a convexly shaped ejecting portion, the convexly shapedejection portion having an ejection height E fulfilling the condition0.010D_(E)<E<0.031D_(E).

In accordance with another aspect of the subject matter of the presentapplication, there is provided an end mill for machining titanium,having a longitudinally extending rotation axis A_(R) and comprising:

-   -   a shank portion, and    -   a cutting portion extending from the shank portion to a cutting        end face and being integrally formed with at least four cutting        teeth alternated with helically shaped flutes and having a        cutting portion diameter D_(E);    -   each tooth comprising    -   a rake surface,    -   a relief surface,    -   a cutting edge formed at an intersection of the rake and relief        surfaces, and    -   a relief edge spaced apart from the cutting edge and formed at        an intersection of the relief surface and an adjacent surface of        the flute succeeding the tooth;    -   each rake surface comprising    -   a rake recessed sub-surface,    -   a rake cutting sub-surface positioned further than the rake        recessed sub-surface from the rotation axis and raised above the        rake recessed sub-surface, relative to an imaginary radial line        passing through the cutting edge, and    -   a rake discontinuity formed at an intersection of the rake        recessed and rake cutting sub-surfaces;    -   wherein each tooth comprises an actual internal cutting angle        formed at an intersection of the rake cutting sub-surface and        the relief surface, the actual internal cutting angle having a        greater value than an imaginary internal cutting angle formed at        an intersection of imaginary extension lines of the rake        recessed sub-surface and the relief surface;    -   wherein, in a plane perpendicular to the rotation axis A_(R),        each flute comprises a convexly shaped ejecting portion and a        concavely shaped bending portion connecting the ejecting portion        and the rake recessed sub-surface;    -   wherein the ejecting portion has an ejection height E which is        measurable between an apex of the ejecting portion to an        imaginary straight line extending from a nadir of the adjacent        bending portion to the adjacent relief edge, the ejection height        E having a magnitude fulfilling the condition        0.010D_(E)<E<0.031D_(E); and    -   wherein, at the cutting end face, index angles of the flutes are        in a symmetric index angle arrangement.

In accordance with still another aspect of the subject matter of thepresent application, there is provided an end mill for machiningtitanium, having a longitudinally extending rotation axis A_(R) andcomprising:

-   -   a shank portion, and    -   a cutting portion extending from the shank portion to a cutting        end face and being integrally formed with at least four cutting        teeth alternated with helically shaped flutes and having a        cutting portion diameter D_(E);    -   each tooth comprising    -   a rake surface,    -   a relief surface,    -   a cutting edge formed at an intersection of the rake and relief        surfaces, and    -   a relief edge spaced apart from the cutting edge and formed at        an intersection of the relief surface and an adjacent surface of        the flute succeeding the tooth;    -   each rake surface comprising    -   a rake recessed sub-surface,    -   a rake cutting sub-surface positioned further than the rake        recessed sub-surface from the rotation axis and raised above the        rake recessed sub-surface, relative to an imaginary radial line        passing through the cutting edge, and    -   a rake discontinuity formed at an intersection of the rake        recessed and rake cutting sub-surfaces;    -   wherein each tooth comprises an actual internal cutting angle        formed at an intersection of the rake cutting sub-surface and        the relief surface, the actual internal cutting angle having a        greater value than an imaginary internal cutting angle formed at        an intersection of imaginary extension lines of the rake        recessed sub-surface and the relief surface;    -   wherein each tooth has a rake cutting sub-surface length        dimension L_(D), measured from the rake discontinuity thereof to        the cutting edge thereof, fulfilling the condition        0.01R_(T)<L_(D)<0.05R_(T), wherein R_(T) is the tooth's radius        dimension, measured in a straight line from the rotation axis to        the cutting edge;    -   wherein each tooth has a radial rake angle within a range of 6°        to −6°;    -   wherein each flute has a helix angle H which fulfills the        condition 30°<H<50°;    -   wherein, in a plane perpendicular to the rotation axis A_(R),        each flute comprises a convexly shaped ejecting portion and a        concavely shaped bending portion connecting the ejecting portion        and the rake recessed sub-surface;    -   wherein the ejecting portion has an ejection height E which is        measurable between an apex of the ejecting portion to an        imaginary straight line extending from a nadir of the adjacent        bending portion to the adjacent relief edge, the ejection height        E having a magnitude fulfilling the condition        0.010D_(E)<E<0.031D_(E); and    -   wherein, at the cutting end face, index angles of the flutes are        in a symmetric index angle arrangement.

It will be understood that the above-said is a summary, and that any ofthe aspects above may further comprise any of the features describedhereinbelow. Specifically, the following features, either alone or incombination, may be applicable to any of the above aspects:

-   A. An ejection height E can have a magnitude which fulfills the    condition 0.014D_(E)<E<0.029D_(E). To elaborate, the range    0.010D_(E)<E<0.031D_(E) is believed to be feasible for machining    titanium, whereas the range 0.014D_(E)<E<0.029D_(E) has achieved    good results during testing. In theory, such moderate ejection    height (i.e. 0.010D_(E)<E<0.031D_(E)) can facilitate a suitable    tooth strength (by allowing a suitable tooth width) and moment of    inertia.-   B. In each plane, of an effective cutting portion of an end mill,    perpendicular to a rotation axis A_(R), an ejecting portion and    bending portion can be present. In each plane, the ejecting portion    can have an ejection height E fulfilling the above mentioned    conditions (i.e., 0.010D_(E)<E<0.031D_(E), or    0.014D_(E)<E<0.029D_(E)).-   C. At least one helix angle can be different from another helix    angle.-   D. A helix angle and an ejecting portion radius of one of the flutes    can be smaller than a respective helix angle and an ejecting portion    radius of another one of the flutes.-   E. Helix angles which are closer to a largest helix angle among the    flutes than to a smallest helix angle among the flutes can be    considered as relatively large helix angles and helix angles which    are closer to a smallest helix angle than to the largest helix angle    among the flutes can be considered as relatively small helix angles.    Each flute with a relatively large helix angle can have an ejecting    portion radius larger than an ejecting portion of each flute with a    relatively small helix angle.-   F. A helix angle and a bending portion radius of one of the flutes    can be smaller than a respective helix angle and a bending portion    radius of another one of the flutes.-   G. Helix angles which are closer to a largest helix angle among the    flutes than to a smallest helix angle among the flutes can be    considered as relatively large helix angles and helix angles which    are closer to a smallest helix angle than to the largest helix angle    among the flutes can be considered as relatively small helix angles.    Each flute with a relatively large helix angle can have a bending    portion radius larger than a bending portion of each flute with a    relatively small helix angle.-   H. A bending portion radius of one of the flutes can be smaller than    an ejecting portion radius thereof. Each flute's bending portion    radius can be smaller than that flute's ejecting portion radius.-   I. Potentially beneficial arrangements of thickening portions for    end mills with a symmetric index angle arrangement can be as    follows. At a cutting end face, only some of the flutes can comprise    a concavely shaped thickening portion connecting an ejecting portion    and relief edge thereof. Such thickening portions can increase tooth    width and hence structural strength needed for machining titanium.    The thickening portions at the end face can decrease in size with    increasing proximity to a shank portion. There may be thickening    portions which start at a position spaced apart from the end face    and which increase in size with increasing proximity to a shank    portion. An end mill can be free of thickening portions that extend    along the entire cutting portion.-   J. At a cutting portion, a core diameter D_(C) can fulfill the    condition 0.47D_(E)<D_(C)<0.60D_(E). The core diameter D_(C) can be    about 0.53D_(E). The prior condition (0.47D_(E)<D_(C)<0.60D_(E)) is    believed to provide a feasible balance between flute size, for chip    evacuation, and acceptable moment of inertia which can provide    acceptable results for machining titanium. In theory, a value closer    to 0.53D_(E) is believed to be optimal and such value has indeed    achieved good results during testing.-   K. An actual internal cutting angle can have a value which differs    from the imaginary internal cutting angle by 4° to 15°. The actual    internal cutting angle can differ from the imaginary internal    cutting angle by 8° to 13°. The prior condition (4° to 15°) is    believed to be feasible for machining titanium. In theory, reducing    the difference (in particular to 8° to 13°) is believed to be    optimal and the latter range has indeed achieved good results during    testing.-   L. Radial rake angles of each tooth can be within a range of 6° to    −6°. Radial rake angles can be about 2° and about −2°. The prior    range (6° to −6°) is believed to be feasible for machining titanium.    In theory, smaller angles (i.e. utilizing radial rake angles smaller    than 6° and −6°) is believed to increase machining performance of    titanium. Indeed, values of about 2° and about −2° achieved good    results during testing.-   M. Teeth of an end mill can be in an arrangement wherein each second    radial rake angle has the same value, which value differs from the    radial rake angle of the alternate teeth. Each second tooth can have    an identical geometry.-   N. Each tooth can have a rake cutting sub-surface length dimension    L_(D), measured from a rake discontinuity to a cutting edge of the    same tooth, fulfilling the condition 0.01R_(T)<L_(D)<0.05R_(T),    wherein R_(T) is the tooth's radius dimension measured in a straight    line from the rotation axis to the cutting edge. A rake cutting    sub-surface length dimension L_(D) can be about 0.026R_(T). The    prior range (0.01R_(T)<L_(D)<0.05R_(T)) is believed to be feasible    for machining titanium. In theory, a cutting sub-surface length    dimension L_(D) value closer to 0.026R_(T) is believed to be optimal    and such value has indeed achieved good results during testing.-   O. At a cutting end face, index angles of the flutes can be in a    symmetric index angle arrangement. Index angles of the flutes can be    in a symmetric index angle arrangement along the entire length of    the cutting portion.-   P. All diametrically opposed index angles at the cutting end face    are of the same magnitude. Index angles at an equal-index-angle    plane P_(E) of the cutting portion can be equal. The    equal-index-angle plane P_(E) can be in the middle of an effective    length of the cutting portion.-   Q. All tooth widths at the cutting end face can have the same    magnitude. Such arrangement facilitates production.-   R. At the cutting end face, each tooth can have a tooth width W_(T)    fulfilling the condition 0.13D_(E)<W_(T)<0.22D_(E). At the cutting    end face, a tooth width W_(T) can be about 0.165D_(E). The prior    range (0.13D_(E)<W_(T)<0.22D_(E)) is believed to be feasible for    machining titanium. In theory, a tooth width W_(T) value closer to    0.165D_(E) is believed to be optimal and such value has indeed    achieved good results during testing.-   S. Each associated rake cutting sub-surface and rake recessed    sub-surface can be arranged relative to one another such that a chip    cut from a workpiece contacts the rake cutting sub-surface, but not    the rake recessed sub-surface immediately adjacent the rake    discontinuity on a side away from the cutting edge.-   T. Each tooth can be free of serrations.-   U. An end mill can have a tool life of at least 60 minutes while    machining titanium, specifically TI6AL4V, at a speed V_(C) of 80.0    meters per minute, a feed rate F_(Z) of 0.08 millimeters per tooth,    a chip thickness a, of 2.00 millimeters, a depth α_(P) of 22.0    millimeters. Under such machining conditions the tool life can be at    least 80 minutes or at least 90 minutes.-   V. Each flute can have a helix angle H which fulfills the condition    30°<H<50°. A helix angle H can be about 35° or about 37°. The prior    range is believed to be feasible for machining titanium. In theory,    the values closer to 35° and 37° are believed to be optimal, and    such values indeed achieved good results during testing. The helix    angles can each be constant or variable (i.e. changing in value at    one or more points, or changing in value at each point along a    length of the cutting portion) along the length of the flute.-   W. Each rake recessed sub-surface can be concavely shaped. Each rake    recessed sub-surface can have an identical shape.-   X. Each flute can be shaped to allow single-pass production thereof    (allowing simpler manufacture than multi-pass production).

BRIEF DESCRIPTION OF THE DRAWINGS

For a better understanding of the subject matter of the presentapplication, and to show how the same may be carried out in practice,reference will now be made to the accompanying drawings, in which:

FIG. 1A is a perspective view of an end mill in accordance with thesubject matter of the present application;

FIG. 1B is a side view of the end mill in FIG. 1A;

FIG. 2A is an end view of the end mill in FIGS. 1A and 1B;

FIG. 2B is a cross-section view taken along line 2B-2B in FIG. 1B;

FIG. 2C is an enlarged view of FIG. 2B with imaginary circles added;

FIGS. 3A and 3B is an enlarged views of cutting edges shown in FIG. 2B;and

FIGS. 4A-4D show test results of end mills including the end mill inFIGS. 1A-3B.

DETAILED DESCRIPTION

Reference is made to FIGS. 1A and 1B, which illustrate an end mill 10,typically made of extremely hard and wear-resistant material such ascemented carbide, configured for machining titanium and for rotatingabout a rotation axis A_(R) extending longitudinally through the centerthereof. In this example the end mill 10 rotation direction D_(R) iscounter-clockwise in the view shown in FIG. 2A.

The end mill 10 comprises a shank portion 12 and a cutting portion 14extending therefrom.

The cutting portion 14 has a cutting portion diameter D_(E) and extendsalong the rotation axis A_(R) in a rearward axial direction D_(B) from acutting end face 16 to a furthermost flute end 18.

The cutting portion 14 is integrally formed with first, second, thirdand fourth teeth 20A, 20B, 20C, 20D, alternated with first, second,third and fourth helically shaped flutes 22A, 22B, 22C, 22D. In thisexample, in addition to identical opposing index angles, there is alsoidentical structure of opposing teeth 20 and opposing flutes 22.

Referring also to FIG. 2A, the index angles I_(A), I_(B), I_(C), I_(D)are in an asymmetric index angle arrangement. The index angles follow arepetitive pattern, with the following values: I_(A)=83°, I_(B)=97°,I_(C)=83°, I_(D)=97°, at the cutting end face 16, having been foundeffective.

Also, as shown in FIG. 2A, first and third teeth 20A, 20C can be shorterthan the second and fourth teeth 20B, 20D, with teeth of each respectivepair both being parallel to each other.

Hereinbelow, similar elements initially differentiated with alphabeticsuffixes (e.g., “20A”, “20B”) may subsequently be referred to in thespecification and claims without such suffixes (e.g., “20”), whenreferring to common features.

Referring also to FIG. 2B, each tooth 20 comprises a relief surface 26A,26B, 26C, 26D a rake surface 28A, 28B, 28C, 28D, a cutting edge 30A,30B, 30C, 30D formed at intersections of the relief and rake surfaces26, 28 and a relief edge 32A, 32B, 32C, 32D formed at intersections ofeach relief surface 26 and an adjacent surface of a succeeding flute 22.In this example, at the cutting end face 16, first and third teeth 20A,20C are succeeded by second and fourth flutes 22B, 22D with second andfourth thickening portions 40B, 40D, described further below, and insuch cases the thickening portion 40 is the closest (adjacent) portionof the succeeding flute 22. Therefore, for example, at the cutting endface 16, the first relief edge 32A is formed at an intersection of thefirst relief surface 26A and the fourth thickening portion's surface40D. Whereas, for example, the second relief edge 32B is formed at anintersection of the second relief surface 26B and a first convexlyshaped ejecting portion 36A, described further below.

The cutting portion 14 has an effective cutting length L extending fromthe cutting end face 16 to a cutting length plane P_(C) extendingperpendicular to the rotation axis A_(R) and positioned where the flutes22 begin to exit (i.e. become more shallow) or where tooth reliefsurfaces 33 are no longer effective. An effective cutting portion isdefined from the cutting end face 16 to the cutting length plane P_(C).

While all diametrically opposed index angles (I) at the cutting end face16 are of the same magnitude, provision of a plane at which the indexangles are equal, namely an equal-index-angle plane P_(E) of the cuttingportion can be equal, as this can simplify manufacture of the end mill10. The equal-index-angle plane P_(E) is believed to have the mostbenefit when being located in the middle of an active cutting portion,i.e. half the distance (L/2) from the cutting end face 16 to the cuttinglength plane P_(C).

The end mill 10 can be gashed, and in this example end gashes 34 areshown in FIG. 2A.

Each flute 22 comprises a convexly shaped ejecting portion 36A, 36B,36C, 36D, a concavely shaped bending portion 38A, 38B, 38C, 38Dconnecting each ejecting portion 36 and each rake surface 28.

Each flute 22 can also comprise a corresponding one of first, second,third and fourth concavely shaped thickening portions 40A, 40B, 40C, 40Dconnecting an associated ejecting portion 36 and relief edge 32 thereof.As shown in FIG. 1A, the third thickening portion 40C (and the identicalfirst thickening portion 40A, not shown) only starts at a positionspaced apart from the cutting end face 16 and increase in size withincreasing proximity to the shank portion 12. As shown in FIG. 2A, thesecond and fourth thickening portions 40B, 40D start at the cutting endface 16, and, as shown in FIG. 1A decrease in size with increasingproximity to the shank portion 12. An arrangement of decreasing andincreasing size of thickening portions 40B can assist in providing toothstrength.

Referring now to FIG. 2C, each ejecting portion 36, bending portion 38and rake recessed sub-surface 48 (described in further detailhereinafter) can be curved and can have a radius R corresponding to aportion of an imaginary circle C. For simplicity, the followingdescription relates to the second flute 22B only, yet correspondingelements and reference characters are understood to be present for eachflute 22 of this example. More precisely: the second rake recessedsub-surface 48B can have a rake radius R_(1B) corresponding to theradius of an imaginary rake circle C_(1B); the second bending portion38B can have a bending radius R_(2B) corresponding to the radius ofimaginary bending circle C_(2B); the second ejecting portion 36B canhave a ejecting radius R_(3B) corresponding to the radius of imaginaryejecting circle C_(3B); and the second thickening portion 40B can have athickening radius R_(4B) corresponding to the radius of imaginarythickening circle C_(4B). Within a flute's cross-section, changes fromone curvature to another can occur at discontinuities therealong. Forexample: a first flute discontinuity 42B can be positioned at anintersection of the second rake recessed sub-surface 48B and the secondbending portion 38B; a second flute discontinuity 44B can be positionedat an intersection of the second bending portion 38B and the secondejecting portion 36B; and a third flute discontinuity 46B can bepositioned at an intersection of the second ejecting portion 36B and thesecond thickening portion 40B.

It will be understood that actual end mill portions may deviate slightlyfrom being perfectly circular. Accordingly, rake recessed sub-potions,bending portions, ejecting portions and thickening portions should beconsidered to approximately have such radii.

Referring to the first flute 22A as an example, measurement of anejection height E is exemplified as follows: the ejection height E_(A)is measurable between an apex A_(A) of the first ejecting portion 36A toan imaginary straight line I_(LA) extending from a nadir N_(A) of theadjacent bending portion 38A (i.e., the nadir N being a closest point ofa bending portion to a center point C_(P) of an end mill) to theassociated, adjacent second relief edge 32B (the second relief edge 32Bdefined for convenience as part of the associated second tooth 20B,however also being associated with the adjacent, succeeding first flute22A).

Each flute 22 has a helix angle H (FIG. 1B) formed with the rotationaxis A_(R). In this example, the helix angle H of first and third flutes22A and 22C is 37° and the helix angle of second and fourth flutes 22Band 22D is 35°. The first and third flutes 22A and 22C having a helixangle H of 37° are considered to have large helix angles, relative tothe second and fourth flutes 22B and 22D having a helix angle H of 35°.

As shown in FIG. 2B, the cutting portion 14 has a core diameter D_(C).The core diameter D_(C) is defined as twice a sum of distances from thecenter point C_(P) to a closest point of each flute 22, divided by thenumber of flutes. In the present example the flutes all have equal depthand consequently the core diameter D_(C) is the diameter of an inscribedcircle C_(I) shown in FIG. 2B. To elaborate, in examples where theflutes have unequal depth, the core diameter D_(C) is twice the averagedistance from the center of an end mill to a closest point of eachflute.

Referring to FIG. 2C, each tooth 20, referring to the first tooth 20A asan example, has a tooth radius R_(TA) and a tooth width W_(TA).

In the example shown, each tooth radius R_(T) has the same magnitude.Consequently, the cutting portion diameter D_(E) is twice the magnitudeof the tooth radius R_(T). In examples where the teeth have unequaltooth radii, the cutting portion diameter D_(E) is defined as twice asum of tooth radii R_(T) divided by the number of teeth.

The tooth width W_(TA) is measurable between a first imaginary lineextending from the center point C_(P) to the cutting edge 30A and asecond imaginary line parallel with the first imaginary line and whichintersects the relief edge 32A.

In the example shown, each tooth width W_(TA) can have the samemagnitude.

For simplicity, the following description is made regarding two teeth20B, 20C only.

Referring to FIGS. 3A and 3B, the rake surfaces 28B, 28C each comprise arake recessed sub-surface 48B, 48C a rake cutting sub-surface 50B, 50Cand a rake discontinuity 52B, 52C formed at an intersection thereof.

To simplify manufacture, the rake recessed sub-surfaces 48 can have thesame shape, which can be a concave shape as shown in FIGS. 3A and 3B.Notably, the shape is recessed from the associated rake cuttingsub-surface 50 so that metal chips which have been cut from a workpiece(not shown) can preferably pass over the rake recessed sub-surfaces 48without contact, especially at points immediately adjacent the rakediscontinuity 52, thereby reducing heat transfer to the end mill.

Each rake cutting sub-surface 50 has an actual internal cutting angleγ_(B), γ_(C) having a greater value than an imaginary internal cuttingangle λ_(B), λ_(C) associated with the rake recessed sub-surface 48 ofthe same tooth 20. More precisely, referring to FIG. 3B as an example,an imaginary rake extension line 53B, extending the second rake recessedsub-surface 48B from the rake discontinuity 52B intersects an imaginaryrelief extension line 55B which extends the second relief surface 26Band forms an acute internal cutting angle λ_(B) at an intersectionthereof.

As best seen in FIGS. 3A and 3B, the cross-section of each rake cuttingsub-surface 50 can be straight.

Each tooth 20 can have a rake cutting sub-surface length dimensionL_(DC) (shown only in FIG. 3A, but existing for each rake cuttingsub-surface 50). In this example, L_(DC) is 0.026R_(T).

Each tooth 20 can have a radial rake angle β measured from an imaginaryradial line L_(R) of the end mill 10 which extends from rotation axisA_(R) to the cutting edge 30, to the rake cutting sub-surface 50.

In the example shown, the radial rake angle β_(B) of the second tooth20B is −2° and the radial rake angle β_(C) of the third tooth 20C is 2°.

The relief surfaces 26 can both form the same radial relief angle α_(B),α_(C), measured relative to an imaginary circular line L_(TB), L_(TC)having the same diameter of the associated tooth 20. In the exampleshown, the radial relief angles α_(B), α_(C) are 7°.

Test results shown in FIGS. 4A to 4D, show comparative tool lives ofdifferent end mills designed for machining titanium. In each instance,tool life was determined by halting machining at predetermined intervals(or upon detecting a rise in power requirements for machining) anddetermining the wear of the tool. Tool failure, after which continuedmachining was halted, was considered to be upon flank wear reaching 0.2mm or corner wear reaching 0.5 mm.

In the tests, end mills numbered as:

-   -   “no. 1” are in accordance with the subject matter of the present        application;    -   “no. 2” have an ejecting portion in accordance with the subject        matter of the present application, but one notable difference to        end mill no. 1 is an asymmetric index angle arrangement;    -   “no. 3” have the same coating as end mill no. 1 and are        similarly free of serrated teeth, but a notable differences        include the cutting edges not being blunt and an asymmetric        index angle arrangement; and    -   “no. 4” have the same coating as end mill no. 1, but notable        differences include serrated teeth, the cutting edges not being        blunt, common helix angles for the entire length of the cutting        portion, and an asymmetric index angle arrangement.

More particularly, FIGS. 4A to 4D each show the results of testing theend mills by cutting a different metal under specific machiningconditions. Table 1 below shows the correspondence between each of FIGS.4A to 4D, regarding the metal being cut and the machining conditions,and Table 2 presents, in tabular form, the test results.

TABLE 1 Tested Materials and Machining Conditions FIG. 4A FIG. 4B FIG.4C FIG. 4D Tested Material Titanium Steel Stainless Steel TI6AL4V AISI4340 Steel 304L DIN 1.2311 Hardness 42 Hardness 190 Hardness 52 (HRc)(HRb) (HRc) speed V_(C) 80.0 180.0 100.0 140.0 (meters/minute) feed rateF_(Z) 0.08 0.08 0.08 0.04 (mm per tooth) chip thickness 2.00 5.00 4.003.00 a_(e) (mm) depth a_(p) (mm) 22.0 20.0 22.0 22.0

TABLE 2 Tool Life (time till halt) for end mills FIG. 4A FIG. 4B FIG. 4CFIG. 4D End mill no. (minutes) (minutes) (minutes) (minutes) 1 110 36 3010 2 100 48 40 10 3 40 62 40 Not tested 4 40 Not tested Not tested 25

The results of the titanium machining test shown in FIG. 4A indicatethat end mill no. 1, which was made in accordance with the subjectmatter of the present application, had the longest tool life. Notably,however, the results seen in FIGS. 4B-4D indicate that this is notevident when machining other materials.

The description above includes an exemplary embodiment which does notexclude non-exemplified embodiments from the claim scope of the presentapplication.

What is claimed is:
 1. An end mill for machining titanium, having alongitudinally extending rotation axis A_(R) and comprising: a shankportion, and a cutting portion extending from the shank portion to acutting end face and being integrally formed with at least four cuttingteeth alternated with helically shaped flutes and having a cuttingportion diameter D_(E); each tooth comprising a rake surface, a reliefsurface, a cutting edge formed at an intersection of the rake and reliefsurfaces, and a relief edge spaced apart from the cutting edge andformed at an intersection of the relief surface and an adjacent surfaceof the flute succeeding the tooth; each rake surface comprising a rakerecessed sub-surface, a rake cutting sub-surface positioned further thanthe rake recessed sub-surface from the rotation axis and raised abovethe rake recessed sub-surface, relative to an imaginary radial linepassing through the cutting edge, and a rake discontinuity formed at anintersection of the rake recessed and rake cutting sub-surfaces; whereineach tooth comprises an actual internal cutting angle formed at anintersection of the rake cutting sub-surface and the relief surface, theactual internal cutting angle having a greater value than an imaginaryinternal cutting angle formed at an intersection of imaginary extensionlines of the rake recessed sub-surface and the relief surface; wherein,in a plane perpendicular to the rotation axis A_(R), each flutecomprises a convexly shaped ejecting portion and a concavely shapedbending portion connecting the ejecting portion and the rake recessedsub-surface; wherein the ejecting portion has an ejection height E whichis measurable between an apex of the ejecting portion to an imaginarystraight line extending from a nadir of the adjacent bending portion tothe adjacent relief edge, the ejection height E having a magnitudefulfilling the condition 0.010D_(E)<E<0.031D_(E); and wherein, at thecutting end face, index angles of the flutes are in a symmetric indexangle arrangement.
 2. The end mill according to claim 1, wherein theejection height E has a magnitude which fulfills the condition0.014D_(E)<E<0.029D_(E).
 3. The end mill according to claim 1, whereinsaid ejecting portion, bending portion and ejection height E, arepresent in each plane perpendicular to the rotation axis A_(R) of aneffective cutting portion of the end mill.
 4. The end mill according toclaim 1, wherein a helix angle and an ejecting portion radius of one ofthe flutes is smaller than a respective helix angle and an ejectingportion radius of another one of the flutes.
 5. The end mill accordingto claim 4, wherein helix angles which are closer to a largest helixangle among the flutes than to a smallest helix angle among the flutesare considered as relatively large helix angles and helix angles whichare closer to a smallest helix angle than to the largest helix angleamong the flutes are considered as relatively small helix angles, andeach flute with a relatively large helix angle has an ejecting portionradius larger than an ejecting portion radius of each flute with arelatively small helix angle.
 6. The end mill according to claim 1,wherein a helix angle and a bending portion radius of one of the flutesis smaller than a respective helix angle and a bending portion radius ofanother one of the flutes.
 7. The end mill according to claim 6, whereinhelix angles which are closer to a largest helix angle among the flutesthan to a smallest helix angle among the flutes are considered asrelatively large helix angles and helix angles which are closer to asmallest helix angle than to the largest helix angle among the flutesare considered as relatively small helix angles, and each flute with arelatively large helix angle has a bending portion radius larger than abending portion radius of each flute with a relatively small helixangle.
 8. The end mill according to claim 1, wherein a bending portionradius of one of the flutes is smaller than an ejecting portion radiusthereof.
 9. The end mill according to claim 8, wherein each flute'sbending portion radius is smaller than that flute's ejecting portionradius.
 10. The end mill according to claim 1, wherein, at the cuttingend face, some, but not all, of the flutes comprise a concavely shapedthickening portion connecting the ejecting portion and the relief edge.11. The end mill according to claim 10, wherein each flute notcomprising a thickening portion at the cutting end face, comprises athickening portion which starts at a position spaced apart from thecutting end face.
 12. The end mill according to claim 11, wherein someof the thickening portions decrease in size and others increase in size,as each thickening portion extends in a direction away from the cuttingend face.
 13. The end mill according to claim 1, wherein at the cuttingportion a core diameter D_(C) fulfills the condition0.47D_(E)<D_(C)<0.60D_(E).
 14. The end mill according to claim 1,wherein the actual internal cutting angle has a value which differs fromthe imaginary internal cutting angle by 4° to 15°.
 15. The end millaccording to claim 1, wherein each tooth has a radial rake angle withina range of 6° to −6°.
 16. The end mill according to claim 1, wherein theteeth are in an arrangement wherein each second radial rake angle hasthe same value, which value differs from the radial rake angle of thealternate teeth.
 17. The end mill according to claim 1, wherein eachtooth has a rake cutting sub-surface length dimension L_(D), measuredfrom the rake discontinuity to the cutting edge of the same tooth,fulfilling the condition 0.01R_(T)<L_(D)<0.05R_(T), wherein R_(T) is therespective tooth's radius dimension.
 18. The end mill according to claim1, wherein all tooth widths at the cutting end face are the samemagnitude.
 19. The end mill according to claim 1, wherein eachassociated rake cutting sub-surface and rake recessed sub-surface arearranged relative to one another such that a chip cut from a workpiececontacts the rake cutting sub-surface, but not the rake recessedsub-surface immediately adjacent the rake discontinuity on a side awayfrom the cutting edge.
 20. The end mill according to claim 1, whereineach tooth is free of serrations.
 21. The end mill according to claim 1,wherein index angles of the flutes have the same magnitude in anequal-index-angle plane P_(E).
 22. The end mill according to claim 1,wherein the end mill has a tool life of at least 60 minutes whilemachining titanium, specifically TI6AL4V, at a speed V_(C) of 262 feet(80.0 meters) per minute, a feed rate F_(Z) of 0.08 millimeters pertooth, a chip thickness a_(e) of 2.00 millimeters, a depth a_(p) of 22.0millimeters.
 23. The end mill according to claim 22, wherein the toollife is at least 80 minutes.
 24. The end mill according to claim 1,wherein each flute has a helix angle H which fulfills the condition30°<H<50°.
 25. The end mill according to claim 1, wherein each tooth, atthe cutting end face, can have a tooth width W_(T) fulfilling thecondition 0.13D_(E)<W_(T)<0.22D_(E).
 26. The end mill according to claim1, wherein each flute is shaped to allow single-pass production thereof.27. An end mill for machining titanium, having a longitudinallyextending rotation axis A_(R) and comprising: a shank portion, and acutting portion extending from the shank portion to a cutting end faceand being integrally formed with at least four cutting teeth alternatedwith helically shaped flutes and having a cutting portion diameterD_(E); each tooth comprising a rake surface, a relief surface, a cuttingedge formed at an intersection of the rake and relief surfaces, and arelief edge spaced apart from the cutting edge and formed at anintersection of the relief surface and an adjacent surface of the flutesucceeding the tooth; each rake surface comprising a rake recessedsub-surface, a rake cutting sub-surface positioned further than the rakerecessed sub-surface from the rotation axis and raised above the rakerecessed sub-surface, relative to an imaginary radial line passingthrough the cutting edge, and a rake discontinuity formed at anintersection of the rake recessed and rake cutting sub-surfaces; whereineach tooth comprises an actual internal cutting angle formed at anintersection of the rake cutting sub-surface and the relief surface, theactual internal cutting angle having a greater value than an imaginaryinternal cutting angle formed at an intersection of imaginary extensionlines of the rake recessed sub-surface and the relief surface; whereineach tooth has a rake cutting sub-surface length dimension L_(D,)measured from the rake discontinuity thereof to the cutting edgethereof, fulfilling the condition 0.01R_(T)<L_(D)<0.05R_(T), whereinR_(T) is the tooth's radius dimension, measured in a straight line fromthe rotation axis to the cutting edge; wherein each tooth has a radialrake angle within a range of 6° to −6°; wherein each flute has a helixangle H which fulfills the condition 30°<H<50°; wherein, in a planeperpendicular to the rotation axis A_(R), each flute comprises aconvexly shaped ejecting portion and a concavely shaped bending portionconnecting the ejecting portion and the rake recessed sub-surface;wherein the ejecting portion has an ejection height E which ismeasurable between an apex of the ejecting portion to an imaginarystraight line extending from a nadir of the adjacent bending portion tothe adjacent relief edge, the ejection height E having a magnitudefulfilling the condition 0.010D_(E)<E<0.031D_(E); and wherein, at thecutting end face, index angles of the flutes are in a symmetric indexangle arrangement.